The Jordan forms of AB and BA∗
Name
Strang E J Linear Algebra 2009.pdf
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124.89 KB
Format
Adobe PDF
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Author(s)
Lippert, Ross A.
Strang, Gilbert
Date Issued
June 2009
Journal
Electronic Journal of Linear Algebra
Publisher
International Linear Algebra Society
Citation
Lippert, Ross A. and Gilbert Strang. "The Jordan Forms of AB and BA*." Electronic Journal of Linear Algebra 18 (2009) : 281-288.
Version
Final published version
Abstract
The relationship between the Jordan forms of the matrix products AB and BA for
some given A and B was first described by Harley Flanders in 1951. Their non-zero eigenvalues and
non-singular Jordan structures are the same, but their singular Jordan block sizes can differ by 1.
We present an elementary proof that owes its simplicity to a novel use of the Weyr characteristic.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
http://www.math.technion.ac.il/iic/ela/ela-articles/articles/vol18_pp281-288.pdf
